Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “mathematical libraries”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Analysis and Benchmarking of feature reduction for classification under computational constraints

Abstract Machine learning is most often expensive in terms of computational and memory costs due to training with large volumes of data. Current computational limitations of many computing systems motivate us to investigate practical approaches, such as feature selection and reduction, to reduce the time and memory costs while not sacrificing the accuracy of classification algorithms. In this work, we carefully review, analyze, and identify the feature reduction methods that have low costs/overheads in terms of time and memory. Then, we evaluate the identified reduction methods in terms of their impact on the accuracy, precision, time, and memory costs of traditional classification algorithms. Specifically, we focus on the least resource intensive feature reduction methods that are available in Scikit-Learn library. Since our goal is to identify the best performing low-cost reduction methods, we do not consider complex expensive reduction algorithms in this study. In our evaluation, we find that at quadratic-scale feature reduction, the classification algorithms achieve the best trade-off among competitive performance metrics. Results show that the overall training times are reduced 61%, the model sizes are reduced 6×, and accuracy scores increase 25% compared to the baselines on average with quadratic scale reduction.

97 MATHEMATICS AND COMPUTING↗

Heracles: Predictive Tools for Opioid Crisis Intervention - m/q Initiative Project Report

The opioid crisis in the United States is being fueled primarily by fentanyl and its molecular analogs, which can be anywhere from 50 to 1,000 times more potent than morphine. Fentanyl itself is straightforward to synthesize; furthermore, the structure is such that fentanyl’s flexible, rotatable side chains are easy to modify to create new analogs. Reference-free computational techniques to predict and identify new fentanyls have the potential to provide a desperately needed preemptive advantage to regulatory stakeholders and toxicologists. The computational pipeline Heracles was developed with this preemptive advantage in mind. Heracles has two primary components: 1) the creation of an in silico library of putative fentanyl analogs, and 2) a downselection pipeline to prioritize generated fentanyl analogs predicted to be potent and easy to synthesize. Experimental observables were also predicted for prioritized analogs, with validation of the observables begun. Heracles has demonstrated potential to aid in the advancement of reference-free paradigms while providing new tools to first responders and other stakeholders attempting to mitigate the opioid crisis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Kokkos Ecosystem [Brief]

In 2016/2017, the field of High-Performance Computing (HPC) entered a new era driven by fundamental physics challenges to produce ever more energy and cost-efficient processors. Since the convergence on the Message-Passing Interface (MPI) standard in the mid-1990s, application developers enjoyed a seemingly static view of the underlying machine — that of a distributed collection of homogeneous nodes executing in collaboration. However, after almost two decades of dominance, the sole use of MPI to derive parallelism acted as a limiter to improved future performance. While MPI is widely expected to continue to function as the basic mechanism for communication between compute nodes for the immediate future, additional parallelism is required on the computing node itself if high performance and efficiency goals are to be realized. When reviewing the architectures of the top HPC systems today, the change in paradigm is clear: the compute nodes of the leading machines in the world are either powered by many-core chips with a few dozen cores each, or use heterogeneous designs, where traditional CPUs marshal work to massively parallel compute accelerators which has as many as 200,000 processing threads in flight simultaneously. Complicating matters further for application developers, each processor vendor has its own preferred way of writing code for their architecture.The Kokkos EcoSystem was released by Sandia in 2017 to address this new era in HPC system design by providing a vendor independent performance portable programming system for scientific, engineering, and mathematical software applications written in the C++ programming language. Using Kokkos, application developers can be more productive because they will not have to create and maintain separate versions of their software for each architecture, nor will they have to be experts in each architecture's peculiar requirements. Instead, they will have a single method of programming for the diverse set of modern HPC architectures. While Kokkos started in 2011 as a programming model only, it soon became clear that complex applications needed more. It is also critical to have a portable mathematical functions and developers need tools to debug their applications, gain insight into the performance characteristics of their codes and tune algorithm performance parameters through automated processes. The Kokkos EcoSystem addresses those needs through its three main components: the Kokkos Core programming model, the Kokkos Kernels math library, and the Kokkos Tools project.

97 MATHEMATICS AND COMPUTING↗

Vistransformers Explained

The Vistransformers Explained library is a collection of python notebooks that demonstrate the internal mechanics and uses of visual-transformer (ViT) machine learning models. The code implements, with mild modifications, ViT models that have been made publicly available through publication and GitHub code. The value added by this code is in-depth explanations of the mathematics behind the sub-modules of the ViT models, including original figures. Additionally, the library contains the code necessary to implement and train the ViT models. The library does not include example training data for the models; instead, it would rely on users generating their own datasets. The code is based on the PyTorch python library. It does not include any files other than python scripts, modules, or notebooks.

Callis, Skylar↗

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗

Practical Probabilistic Programming

Recent advances in probabilistic programming languages (PPLs) have provided the capability for exact inference: computing a closed-form probability distribution for a given probabilistic program. In particular, the new language Roulette uses a language oriented programming (LOP) approach, wherein analysts build new programming languages on top of a set of primitives provided by Roulette, which then translates these structures into a weighted model counting problem which can be solved by automated reasoning tools. However, because Roulette provides few convenience features, developing these new languages is challenging even for expert users. We developed a standard library of common probability functions for Roulette with the goal of improved usability. This included approximation of continuous probability density functions using discrete probability mass functions. We demonstrated this approach by modeling a cosmic ray striking a RAM controller. We found that Roulette provides a powerful interface for highly expressive probabilistic programs to be generated. In collaboration with the NNSA Advanced Simulation and Computing program, which resulted in development of a tool called Circulette, we were able to model complex circuits expressed in Verilog using probabilistic programs with an expressivity not previously possible. Our research question that motivated the development of a Roulette standard library was to determine whether non-experts could use a PPL to model relevant problems regarding radiation effects on microelectronics. This standard library improved the expressivity of Roulette by implementing common probability density functions, mathematical operators on distributions, and support for empirical distributions. While Roulette is a powerful modeling language, the untyped, LOP approach makes error messages difficult to understand and requires expert aid. We recommend further research on Roulette, especially with its error messages, to enable improved usability. At the same time, this project demonstrated that for users familiar with Roulette and the LOP approach, Roulette provides powerful new capabilities that can be integrated with other Sandia modeling capabilities.

97 MATHEMATICS AND COMPUTING↗

Challenges of and Opportunities for a Large Diverse Software Team

A large software team consisting of members with different expertise, skillsets, personalities, ethnicities, and involving collaboration on a large and complex software product presents many technical and cultural challenges, but also provides unique opportunities. In this article, we discuss the essential issues we faced when successfully transforming a collection of various independently developed software libraries into one large integrated product: the eXtreme-scale scientific Software Development Kit (xSDK). Furthermore, we argue it is just as important to pay attention to cultural challenges, such as establishment of reliable communication channels that considers, among others, differences in personalities and backgrounds as well as overcoming geographical separation and time-zone distribution when collaborating, as technical challenges. Finally, we discuss opportunities stemming from participating in a large diverse software team, such as increased internal expertise, variety of skillsets, broadened connections to external experts, and access to a larger pool of ideas or solutions.

97 MATHEMATICS AND COMPUTING↗

MAGMA: Enabling exascale performance with accelerated BLAS and LAPACK for diverse GPU architectures

MAGMA (Matrix Algebra for GPU and Multicore Architectures) is a pivotal open-source library in the landscape of GPU-enabled dense and sparse linear algebra computations. With a repertoire of approximately 750 numerical routines across four precisions, MAGMA is deeply ingrained in the DOE software stack, playing a crucial role in high-performance computing. Notable projects such as ExaConstit, HiOP, MARBL, and STRUMPACK, among others, directly harness the capabilities of MAGMA. In addition, the MAGMA development team has been acknowledged multiple times for contributing to the vendors’ numerical software stacks. Looking back over the time of the Exascale Computing Project (ECP), we highlight how MAGMA has adapted to recent changes in modern HPC systems, especially the growing gap between CPU and GPU compute capabilities, as well as the introduction of low precision arithmetic in modern GPUs. We also describe MAGMA’s direct impact on several ECP projects. Maintaining portable performance across NVIDIA and AMD GPUs, and with current efforts toward supporting Intel GPUs, MAGMA ensures its adaptability and relevance in the ever-evolving landscape of GPU architectures.

97 MATHEMATICS AND COMPUTING↗

Expansion of the Verified, Archived, Library of Inputs and Data (VALID) [Slides]

This project dialogue provides an update on the Expansion of Verified, Archived, Library of Inputs and Data or VALID. VALID is a QA-Like (Quality Assurance) process to generate high quality models from reliable reference descriptions and make those models available to users. This presentation provides a brief project overview, a reminder of cases added in FY2021, cases currently in progress, and future plans for VALID.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Translational research in the MPICH project

The MPICH project is an example of translational research in computer science before that term was well known or even coined. The project began in 1992 as an effort to develop a portable, high-performance implementation of the emerging Message-Passing Interface (MPI) Standard. It has enabled the widespread adoption of MPI as a way to write scalable parallel applications on systems of all sizes including upcoming exascale supercomputers. In this paper, we describe how the translational research process was used in MPICH, how that led to its success, the challenges encountered and lessons learned, and how the process could be applied to other similar projects.

97 MATHEMATICS AND COMPUTING↗

GNDS v2.0 release and future developments [Slides]

This presentation begins by discussing the major changes in v2.0 of GNDS and that the GNDS-2.0 formatted libraries are now available. It also examines how code support for GNDS is growing with processing codes, APIs and transport codes, and evaluation/testing codes. The presentation states that while migrating to GNDS can be a major effort it worthwhile, especially for anyone who is just getting started as nuclear data creator or user. Additionally, this presentation outlines the established milestones that the EG-GNDS (the group in charge of GNDS specs) has for the next GNDS release and elaborates on the first goal, which is to migrate GNDS specifications to the new JSON schema language.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

ZMPY3D: accelerating protein structure volume analysis through vectorized 3D Zernike moments and Python-based GPU integration

Abstract Motivation Volumetric 3D object analyses are being applied in research fields such as structural bioinformatics, biophysics, and structural biology, with potential integration of artificial intelligence/machine learning (AI/ML) techniques. One such method, 3D Zernike moments, has proven valuable in analyzing protein structures (e.g., protein fold classification, protein–protein interaction analysis, and molecular dynamics simulations). Their compactness and efficiency make them amenable to large-scale analyses. Established methods for deriving 3D Zernike moments, however, can be inefficient, particularly when higher order terms are required, hindering broader applications. As the volume of experimental and computationally-predicted protein structure information continues to increase, structural biology has become a “big data” science requiring more efficient analysis tools. Results This application note presents a Python-based software package, ZMPY3D, to accelerate computation of 3D Zernike moments by vectorizing the mathematical formulae and using graphical processing units (GPUs). The package offers popular GPU-supported libraries such as CuPy and TensorFlow together with NumPy implementations, aiming to improve computational efficiency, adaptability, and flexibility in future algorithm development. The ZMPY3D package can be installed via PyPI, and the source code is available from GitHub. Volumetric-based protein 3D structural similarity scores and transform matrix of superposition functionalities have both been implemented, creating a powerful computational tool that will allow the research community to amalgamate 3D Zernike moments with existing AI/ML tools, to advance research and education in protein structure bioinformatics. Availability and implementation ZMPY3D, implemented in Python, is available on GitHub (https://github.com/tawssie/ZMPY3D) and PyPI, released under the GPL License.

Lai, Jhih-Siang (ORCID:0000000156775890)↗

Parallel Element-based Algebraic Multigrid for H (c url ) and H (div) Problems Using the ParELAG Library

This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H (c url ) and H (div) formulations. ParELAG constructs hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗

On ParELAG's Parallel Element-based Algebraic Multigrid and its MFEM Miniapps for H(curl) and H(div) Problems: a report including lowest and next to the lowest order numerical results

This paper presents the utilization of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H(curl) and H(div) formulations. This involves the construction of hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

16 TIDAL AND WAVE POWER↗

JOINT APPOINTEE: Evolution of ferroelectric properties in SmxBi1-xFeO3 via automated Piezoresponse Force Microscopy across combinatorial spread libraries

Combinatorial spread libraries offer a innovative approach to explore the evolution of material properties over broad concentration, temperature, and growth parameter spaces. However, traditional limitation of this approach is the requirement for the read-out of functional properties across the library. Here we develop automated Piezoresponse Force Microscopy (PFM) for the exploration of combinatorial spread libraries and demonstrate its application in the SmxBi1-xFeO3 system with the ferroelectric-antiferroelectric morphotropic phase boundary. This approach relies on the synergy of the quantitative nature of PFM and the implementation of automated experiments that allow PFM-based sampling over macroscopic samples. The concentration dependence of pertinent ferroelectric parameters has been determined and used to develop the mathematical framework based on Ginzburg-Landau theory describing the evolution of these properties across the concentration space. We pose that a combination of automated scanning probe microscope and combinatorial spread library approach will emerge as an efficient research paradigm to close the characterization gap in the high-throughput materials discovery. We make the data sets open to the community and hope that this will stimulate other efforts to interpret and understand the physics of these systems.

Automated Microscopy, Combinatorial Library, Ferro↗